These teachings relate generally to a computer implemented physical signal analysis method and apparatus, such as, but not limited to, biophysical and geophysical, imaging and speech, signal analysis method and apparatus.
Analyzing typical physical signals is a difficult problem confronting many industries. Industries have harnessed various computer implemented methods to process data taken from biophysical phenomena, such as, but not limited to, electrocardiogram signals, signals from esophageal manometric data, ultrasound data such as, data from fetal heart monitor, data from geophysical phenomena such as earthquakes, ocean waves, tsunamis, ocean surface elevation and wind, images and also speech data.
Among the difficulties is that representing physical processes with physical signals may present one or more of the following problems:
(a) The total data span is too short;
(b) The data are nonstationary; and
(c) The data represent nonlinear processes.
Computer implemented Empirical Mode Decomposition method which decomposes physical signals representative of a physical phenomenon into components have been effective in the analysis of physical signals. These components are designated as Intrinsic Mode Functions (IMFs) and are indicative of intrinsic oscillatory modes in the physical phenomenon. The basic EMD method is disclosed in U.S. Pat. No. 5,983,162 and U.S. Pat. No. 6,311,130, both of which are incorporated by reference herein in their entirety for all purposes.
Some examples of signals from physical processes are given below.
Earthquake Signals
Earthquakes are typically recorded by seismometers such as the seismometer 400 which may be implemented with the Ranger seismometer manufactured by kinemetrics Model WR-1 Wide-Band which records ground accelerations to produce a signal representative of the earthquake.
Fortunately, all earthquakes are transient lasting only a few tenths to a few seconds at most; consequently, earthquake signals are nonstationary. Most earthquake signals are still processed with various computer implemented methods that apply algorithms based on Fourier analysis (Hu, et al. Earthquake Engineering, Chapman & Hall, London, 1996). Such earthquake signals are processed to better understand, for example, crust structure geophysics, near field earthquakes and site specific ground motions.
Crust structure geophysics is a term for the geophysical structure of the earth which includes the crust and inner core. Due to the different geophysical properties of the local crust material, the earthquake signal can be used to determine the mode of earthquake wave propagation, their dispersion characteristics, and the free oscillations. These properties can be used to infer the structure of the crust, and the elastic properties and density of the crust medium through which the wave propagated.
Most seismologists are interested in the earthquake signals to infer the geophysical properties of the earth as explained above. Earthquake engineers, however, are interested in the destructive power of the earthquakes. Therefore, the seismologists prefer sampling the earthquake signal from a long distance, up to thousand of miles say, to infer the geophysical properties of the crust along the path of wave propagation. On the other hand, earthquake engineers are most interested in the immediate neighborhood of the earthquake epicenter (near field earthquakes), within a few kilometers say, where the destruction would be the most severe.
For any given earthquake, the ground response is site specific and depends on the following factors: (1) nature of the earthquake (whether it is a shear or a thrust), (2) the propagation path, (3) the local ground geo-engineering properties (whether it is rock or sediment), and (4) the local topographic geometry (e.g., whether in a valley or on the top of a hill). These factors influence the severity of the ground motion from a given earthquake at specific locations.
Conventional methods, however, cannot reveal detailed information in the dispersion properties, the wave form deformation, and the energy-frequency distribution of earthquakes because the data representing the earthquake is nonlinear and nonstationary. Revealing this information is necessary to correctly understand crust structure geophysics and to accurately deduce site specific ground motions.
Furthermore, most near field strong earthquake ground motions are nonstationary because of their extremely short duration. Seismic records representing such earthquakes always give artificially wide Fourier spectra because of this nonstationarity. This wide frequency distribution will dilute the energy content everywhere on the frequency axis and distort the true energy-frequency distribution. The result is that the energy density at critical resonant frequencies for specific building structures will be underestimated. The rule of thumb for the resonant frequency is given as 1/(0.1N) cycle per second, where N is the number of the stories of the building. Therefore, for a ten-story building, the resonant frequency is near 1 Hz. For high-rises, the frequency will be even lower.
Water Wave Signals
The dynamics of ocean waves are measured from ocean sensors located at field stations such as the ocean wave sensor 410 which may be implemented by using the NDBC 3m discus ocean wave sensor which records an ocean wave signal representing ocean surface elevation as a function of time. Ocean waves are studied for ship design, ship routing, coastal and off-shore structure design, harbor operations, and even weather forecasting.
Ocean wave signals are typically random and nearly nonstationary. In the past, ocean wave signals were analyzed by applying computer implemented Fourier analysis. In fact, the studies of the wave spectra from Fourier analysis have been a main subject of ocean wave research (see, for example, Huang, et al., 1990a, Wave Spectra, The Sea, 9, 197-237).
Traditional computer implemented analysis methods, however, are not well suited to studying ocean wave signals because ocean waves are typically nonlinear and nonstationary. The Wavelet spectrum gives a nearly continuous distribution, and wide spread of energy consisting primarily of harmonics in the frequency axis. This energy spread is due to the nonlinear and nonstationary character of ocean waves. This energy spread also contributes to the difficulty in analyzing the results of traditional computer implemented techniques applying the Wavelet transform.
Water wave signals detected from mechanically generated water waves by a wave sensor have been studied to analyze nonlinear water wave evolution processes (eg. Huang, et al., The Mechanism for Frequency Downshift in Nonlinear Wave Evolution, Advances in Applied Mechanics, Vol. 32, pp. 59-117 1996).
Due to weak nonlinear interactions, the frequency of the water waves will downshift as they propagate, a process necessary for the waves to become longer and grow higher under the wind.
In the narrow-band wave field, the downshift has been shown as the consequence of the Benjamin-Fier instability (Benjamin and Fier, The Disintegration of Wavetrains on Deep Water, Part I, Theory, J. Fluid Mech., 27, 417-430, 1967). Although water wave evolution is generally assumed to be gradual and continuous, several authors have theorized that the evolution is not continuous and gradual, but local and discrete.
The resolution power of previous data analysis techniques, however, has rendered proof of this theory nearly impossible. As explained above, computer implemented data analysis techniques, prior to the use of EMD, were incapable of accurately interpreting nonlinear, nonstationary processes such as water wave propagation and evolution.
Tsunami Signals
Tsunamis are detected with tidal gauges such as the tidal gauge 430 which record water elevation as a function of time.
Although tidal signals are generally stationary, tsunami waves are transient, nonlinear and nonstationary. Tidal gauges necessarily measure both the tide and the tsunami. The combined signal, therefore, is nonstationary and nonlinear.
Filtering cannot remove the tsunami signal cleanly because the tsunami signals and the tidal signals usually have many harmonic components in the same frequency range. Therefore, tsunami signals and combined tsunami-tidal signals, prior to the use of EMD, lacked an effective computer implemented data analysis method which is able to handle the nonlinear and nonstationary character of the data representative of these geophysical processes.
Ocean Altitude and Ocean Circulation
Satellite altimetry is a powerful technique for large scale ocean circulation studies (Huang, et al. 1978, “Ocean Surface Measurement Using Elevation From GEOS-3 Altimeter”, J. Geophys. Res., 83, 4, 673-4, 682; Robinson, et al., 1983, “A Study of the Variability of Ocean Currents in the Northwestern Atlantic Using Satellite Altimetry”, J. Phys. Oceanogr., 13, 565-585). An orbital satellite system can produce extremely accurate data representing the altitude of the ocean surface.
The accepted view of the equatorial dynamics is the propagation of Kelvin waves forced by variable wind stress (Byod, 1980, “The Nonlinear Equatorial Kelvin Waves”, J. Phys. Oceanogr., 10, 1-11 and Zheng, et al., 1995, “Observation of Equatorially Trapped Waves in the Pacific Using Geosat Altimeter Data”, Deep-Sea Res., (in press). In this model, the wave propagation will leave a surface elevation signature of the order of 10 cm, which can be measured by the satellite altimeter 440.
Because of the importance of the equatorial region in determining the global climate pattern, altimeter data have been used extensively to study the dynamics of this region (Miller, et al., 1988, “GEOSAT Altimeter Observation of Kelvin Waves and the 1986-1987 El Nino” Science, 239, 52-54; Miller, et al., 1990, “Large-Scale Meridional Transport in the Tropic Pacific Ocean During the 1986-87 El Nino from GEOSAT”, J. Geophys. Res. 95, 17, 905-17, 919.; Zheng, et al., 1994, “The Effects of Shear Flow on Propagation of Rossby Waves in the Equatorial Oceans”, J. Phys. Oceanogr., 24, 1680-1686 and Zheng, et al., 1995, “Observation of Equatorially Trapped Waves in the Pacific Using Geosat Altimeter Data”, Deep-Sea Res., (in press)). A typical time series on the Equator sea surface elevation data at 174.degree.
Limited by the data length and complicated by ocean dynamics, all the past investigators, prior to their use of EMD, faced serious problems in processing this nonstationary altimeter data. Therefore, weather forecasting which accurately accounts for ocean effects has been impossible with traditional computer implemented data analysis methods.
Ultrasound Fetal Heart Monitoring
The application of EMD to ultrasound Doppler fetal heart monitoring is described in Rouvre, D.; Kouame, D.; Tranquart, F.; Pourcelot, L, Empirical mode decomposition (EMD) for multi-gate, multi-transducer ultrasound Doppler fetal heart monitoring, Proceedings of the Fifth IEEE International Symposium on Signal Processing and Information Technology, 2005, which is incorporated by reference herein is entirety for all purposes. As stated in that paper, “Ultrasound (US) Doppler provides both detection of the FHR and fetal movements of the fetus, thus providing more information on fetal well-being, and is widely used for FHR monitoring. Whether mono or bi-transducer, these systems using continuous or pulsed ultrasound waves provide partial automated detection of movements and fetal breathing . . . . Classical [before EMD] autocorrelation based Fetal HeartRate (FHR) detection is not always satisfactory.” See also Nimunkar, A. J., Tompkins, W. J., EMD-based 60-Hz noise filtering of the ECG, 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2007. EMBS 2007, Page(s): 1904-1907; Hualou Liang, Qiu-Hua Lin, Chen, J. D. Z.; Application of the empirical mode decomposition to the analysis of esophageal manometric data in gastroesophageal reflux disease, IEEE Transactions on Biomedical Engineering, Volume: 52 Issue: 10 Date: October 2005, Page(s): 1692-1701, all of which are incorporated by reference herein in their entirety for all purposes.
Speech Signals
Speech signals are nonstationary, which makes them less amenable to Fourier analysis. Speech signals have been decomposed into different oscillatory modes, IMFs, utilizing EMD. The resonant frequencies of the vocal tract can then be extracted in order to obtain a description of the speech production model. See, for example, Aicha Bouzid, Noureddine Ellouze, EMD Vocal Tract Frequency Analysis of Speech Signal, 4th International Conference: Sciences of Electronic, Technologies of Information and Telecommunications, Mar. 25-29, 2007—TUNISIA; Khaldi, K., Boudraa, A.-O., Bouchikhi, A, Alouane, M. T.-H., Diop, E.-H. S., Speech signal noise reduction by EMD, 2008. ISCCSP 2008, 3rd International Symposium on Communications, Control and Signal Processing, Page(s): 1155-1158, which are Incorporated by reference herein in their entirety for all purposes.
Images
EMD has also been utilized in analysis of images, such as texture extraction and image filtering. See, for example, J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, Ph. Bunel, Image analysis by bidimensional empirical mode decomposition, Image and Vision Computing 21 (2003) 1019-1026, which is incorporated by reference herein in its entirety for all purposes.
Although the EMD method has been applied for different physical signals, the EMD method fails in many cases where the data contains two or more frequencies are close to each other. Unfortunately this condition is typical of many physical signals.
Therefore, there is a need for improved EMD methods.